Newton's second law says $F=ma$.
Now if we put $F=0$ we get $a=0$ which is Newton's first law.
So why do we need Newton's first law ?
Before asking I did some searching and I got this: Newtons first law is necessary to define inertial reference frame on which the second law can be applied.
But why can't we just use Newton's second law to define an inertial frame? So if $F=0$ but $a$ is not equal to 0 (or vice versa), the frame is non-inertial.
One can say (can one?) we cannot apply the second law to define a reference frame because it is only applicable to inertial frames. Thus unless we know in advance that a frame is inertial, we can't apply the second law.
But then why this is not the problem for the first law?
We don't need to know it in advance about the frame of reference to apply the first law. Because we take the first law as definition of an inertial reference frame.
Similarly if we take the second law as the definition of an inertial frame, it should not be necessary to know whether the frame is inertial or not to apply the second law (to check that the frame is inertial).
Best Answer
I don't think this is obvious from Newton's statement of the Second Law. In his Principia Mathematica, Newton says that a force causes an acceleration. Without the first law, this doesn't necessarily imply that zero force means zero acceleration. One could conceive of other things that also cause acceleration.
A modern person might be concerned about non-inertial reference frames. Someone from Newton's time would probably be more concerned about Aristotelian ideas of objects seeking their own level. But in either case, its necessary to emphasize that forces not only cause acceleration, but that they are the only things that do so (or in the modern formulation, that there exists a frame in which they are the only things that do so).